Question:
Five men go to a restaurant together and each of them orders a dish that is different from the dishes ordered by the other members of the group. However, the waiter serves the dishes randomly. Then the probability that exactly one of them gets the dish he ordered equals __________ (round off to 2 decimal places)
Five men go to a restaurant together and each of them orders a dish that is different from the dishes ordered by the other members of the group. However, the waiter serves the dishes randomly. Then the probability that exactly one of them gets the dish he ordered equals __________ (round off to 2 decimal places)
Updated On: Oct 1, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 0.35
Solution and Explanation
The correct answer is 0.35 to 0.40.(approx)
Was this answer helpful?
0
0
Top Questions on Testing of Hypotheses
- Let \( X_1, X_2, \ldots, X_n \) be a random sample from an \( \text{Exp}(\lambda) \) distribution, where \( \lambda \in \{1, 2\} \). For testing \( H_0: \lambda = 1 \) against \( H_1: \lambda = 2 \), the most powerful test of size \( \alpha \), \( \alpha \in (0,1) \), will reject \( H_0 \) if and only if
- IIT JAM MS - 2024
- Statistics
- Testing of Hypotheses
- Let \( X_1, X_2, \ldots, X_{10} \) be a random sample from a \( N(0, \sigma^2) \) distribution, where \( \sigma > 0 \) is unknown. For testing \( H_0: \sigma^2 \leq 1 \) against \( H_1: \sigma^2 > 1 \), a test of size \( \alpha = 0.05 \) rejects \( H_0 \) if and only if \( \sum_{i=1}^{10} X_i^2 > 18.307 \). Let \( \beta \) be the power of this test, at \( \sigma^2 = 2 \). Then \( \beta \) lies in the interval
(You may use \( \chi^2_{10,0.05} = 18.307 \), \( \chi^2_{10,0.1} = 15.9872 \), \( \chi^2_{10,0.25} = 12.5489 \), \( \chi^2_{10,0.5} = 9.3418 \), \( \chi^2_{10,0.75} = 6.7372 \), \( \chi^2_{10,0.9} = 4.8652 \), \( \chi^2_{10,0.95} = 3.9403 \), \( \chi^2_{10,0.975} = 3.247 \))- IIT JAM MS - 2024
- Statistics
- Testing of Hypotheses
- Let 𝑋1,𝑋2,𝑋5 be a random sample from a 𝐵𝑖𝑛(1, 𝜃) distribution, where 𝜃∈(0,1) is an unknown parameter. For testing the null hypothesis 𝐻0 ∶ 𝜃≤ 0.5 against 𝐻1 :𝜃>0.5, consider the two tests 𝑇1 and 𝑇2 defined as:
𝑇1: Reject 𝐻0 if, and only if, \(∑^5_{i=1}\) 𝑋𝑖=5.
𝑇2: Reject 𝐻0 if, and only if, \(∑^5_{i=1}\) Xi≥3.
Let 𝛽𝑖 be the probability of making Type-II error, at 𝜃=\(\frac{2}{3}\), when the test 𝑇𝑖 , 𝑖=1,2 , is used. Then, the value of 𝛽1+𝛽2 equals ________(round off to two decimal places)- IIT JAM MS - 2023
- Statistics
- Testing of Hypotheses
- Let 𝑥1, 𝑥2, 𝑥3 and 𝑥4 be observed values of a random sample from an 𝑁(𝜃, 𝜎 2 ) distribution, where 𝜃∈ℝ and 𝜎>0 are unknown parameters. Suppose that 𝑥̅=\(\frac{1}{4} ∑^4_{i=1} 𝑥_𝑖 = 3.6 \) and \(\frac{1}{3} ∑^4_{i=1} (𝑥_𝑖-\overline{x} )^2= 20.25\) . For testing the null hypothesis 𝐻0 ∶ 𝜃=0 against 𝐻1 ∶𝜃≠0, the 𝑝-value of the likelihood ratio test equals
- IIT JAM MS - 2023
- Statistics
- Testing of Hypotheses
- Let X1, X2 ,…, X25 be a random sample from a 𝑁(μ, 1) distribution, where μ ∈ \(\R\) is unknown. Consider testing of the hypothesis H0 : μ = 5.2 against H1 : μ = 5.6. The null hypothesis is rejected if and only if \(\frac{1}{25}\sum^{25}_{i=1}X_i > k\) , for some constant k. If the size of the test is 0.05, then the probability of type-II error equals __________ (round off to 2 decimal places)
- IIT JAM MS - 2022
- Statistics
- Testing of Hypotheses
View More Questions
Questions Asked in IIT JAM MS exam
- A bag has 5 blue balls and 15 red balls. Three balls are drawn at random from the bag simultaneously. Then the probability that none of the chosen balls is blue equals
- IIT JAM MS - 2024
- Probability
- Let the random vector \( (X, Y) \) have the joint probability density function
\[f(x, y) = \begin{cases} \frac{1}{x}, & \text{if } 0 < y < x < 1 \\0, & \text{otherwise} \end{cases}.\]
Then \( \text{Cov}(X, Y) \) is equal to:- IIT JAM MS - 2024
- Probability
- Two factories \( F_1 \) and \( F_2 \) produce cricket bats that are labelled. Any randomly chosen bat produced by factory \( F_1 \) is defective with probability 0.5 and any randomly chosen bat produced by factory \( F_2 \) is defective with probability 0.1. One of the factories is chosen at random, and two bats are randomly purchased from the chosen factory. Let the labels on these purchased bats be \( B_1 \) and \( B_2 \). If \( B_1 \) is found to be defective, then the conditional probability that \( B_2 \) is also defective is equal to __________ (round off to 2 decimal places).
- IIT JAM MS - 2024
- Probability
- Consider a coin for which the probability of obtaining head in a single toss is \( \frac{1}{3} \). Sunita tosses the coin once. If head appears, she receives a random amount of \( X \) rupees, where \( X \) has the \( \text{Exp}\left( \frac{1}{9} \right) \) distribution. If tail appears, she loses a random amount of \( Y \) rupees, where \( Y \) has the \( \text{Exp}\left( \frac{1}{3} \right) \) distribution. Her expected gain (in rupees) is equal to __________ (answer in integer).
- IIT JAM MS - 2024
- Probability
- If 12 fair dice are independently rolled, then the probability of obtaining at least two sixes is equal to __________ (round off to 2 decimal places)
- IIT JAM MS - 2024
- Probability
View More Questions